Question

describe the error in finding m∠s.
given △qrs ≅ △xzy
∠s ≅ ∠z
m∠s = m∠z
m∠s = 42°
the triangle sum theorem should be used to ensure that
both triangles are right triangles
the angle measures are possible
corresponding parts are matched up correctly
correct the error.

Explanation:

Step1: Analyze the error

The error is that the person directly assumed \(m\angle S = m\angle Z\) without considering the properties of right - angled triangles. In \(\triangle XZY\), \(\angle Z\) is not the non - right angle shown as \(42^{\circ}\).

Step2: Use the correct method

Since \(\triangle QRS\cong\triangle XZY\), \(\angle S\) corresponds to \(\angle Y\) (because of the order of congruence \(\triangle QRS\cong\triangle XZY\), \(S\) corresponds to \(Y\)). In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\). In \(\triangle XZY\), if one non - right angle is \(42^{\circ}\), then \(m\angle Y=90^{\circ}- 42^{\circ}\).

Answer:

The error is that the wrong corresponding angle was used. \(m\angle S = 90^{\circ}-42^{\circ}=48^{\circ}\)